The present invention relates to multilevel coded modulation useful, for example, in wireless, or cellular, environments.
In trellis coded modulation (xe2x80x9cTCMxe2x80x9d) schemes, trellis coding and modulation are combined such that a number of information bits are caused to be represented by a symbol which is modulated onto a carrier for transmission over a communications channel. The symbol is taken from a predetermined symbol constellation which is partitioned into a number of subsets. A particular symbol is selected to represent the information bits by first providing a portion of the information bits to a trellis encoder. The output of the encoder is used to select a subset of the constellation. The remaining, so-called uncoded, information bits are then used to select the particular symbol from the selected subset.
In particular, upon receiving a portion of the information bits, the trellis encoder, a finite state machine, transitions from a current to a next state and, as a consequence, generates the bits that identify a subset. The number of states that a trellis encoder may assume directly affects the computational burden on a receiver to recover the transmitted signal. Thus, the greater number of states of a code, the more complex the code is said to be.
It is a characteristic of trellis encoders that only certain encoder state transitions are allowed. As a result, only certain sequences of subsetsxe2x80x94referred to as valid sequences of subsetsxe2x80x94are allowed by the code to occur. A further result, then, is that only certain sequences of symbols taken from those subsetsxe2x80x94referred to as valid sequences of symbolsxe2x80x94are allowed by the code to occur. The error performance of any given TCM scheme is determined in part by its so-called minimum distance. This is the minimum of the distance between any two valid sequences of symbols, that distance being given by the square root of the sum of the squares of the distance between each corresponding pair of symbols of the two sequences.
An N-dimensional TCM scheme, in particular, utilizes N-dimensional symbols taken from a N-dimensional constellation. The N-dimensional constellation is typically comprised of a concatenation of a number of constituent lower-dimensionality constellations and each N-dimensional symbol is thus comprised of a number of lower-dimensionality signal points, which are transmitted during respective signaling intervals. The N-dimensional constellation is partitioned into N-dimensional subsets which is typically based on a partition of its constituent lower-dimensional constellation into lower-dimensional signal point subsets. Each N-dimensional subset may be comprised of several concatenations of lower-dimensional signal point subsets. As a consequence of the above, the fact that the trellis encoder allows only certain valid sequences of N-dimensional subsets means that only certain sequences of the aforementioned lower-dimensional signal point subsets are valid. Likewise, the fact that the trellis encoder allows only certain valid sequences of N-dimensional symbols means that only certain sequences of the aforementioned lower-dimensional signal points are valid. Typically, the signal points are two-dimensional (2D) signal points.
A TCM scheme is also characterized by a certain level of so-called time diversity. This parameter is equal to the minimum number of signal point positions in any two valid sequences of signal points at which the signal points are different. For example, the coding scheme has a time diversity of xe2x80x9c2xe2x80x9d if, given any two valid sequences of signal points, the number of signal point positions at which the signal points are different is at least equal to 2. Having a time diversity of xe2x80x9c2xe2x80x9d or more is advantageous in, for example, wireless environments, which are typically characterized by so-called fading channels, i.e., channels in which the signal amplitude can become too weak to carry any useful information about the transmitted signal. Nevertheless, with the time diversity of at least xe2x80x9c2xe2x80x9d, it is still possible to recover the transmitted signal in the presence of deep fade.
In designing a specific TCM scheme, a number of parameters are traded off against each other depending on the design criteria. Among the most significant of these are bandwidth efficiency (this being the number of information bits represented by each symbol), and three of the parameters noted abovexe2x80x94the complexity of the code, its minimum distance, and its level of time diversity.
Thus, consider the case of a coding scheme which has acceptable bandwidth efficiency, code complexity and minimum distance but does not have a desired level of time diversity for a wireless communications application. One way to increase the level of time diversity is to use a very fine partition of the constellation and an encoder having a greater number of states. As noted above, however, this gives rise to increased decoder complexity. It may also decrease the minimum distance. Another possible way to increase time diversity involves reducing the number of symbols in each subset to a lower number, thereby reducing the total number of symbols in the constellation. However, this reduces the number of the aforementioned uncoded bits that are represented by each symbol, thus reducing the bandwidth efficiency.
The present invention provides for increased time diversity while sacrificing one or more other performance parameters only to a slight extent. Coding schemes embodying the principles of the invention are so-called multilevel coded modulation schemes of a type generally known in the art comprised of a so-called first-level code and a so-called second-level code, each code receiving respective portions of the input data stream. The first-level code in and of itself does not provide the overall code with a desired level of time diversity. In accordance with the invention, however, the second-level code is chosen such that the overall code does exhibit that desired level of time diversity.
In preferred embodiments, the first-level code is a N-dimensional trellis code with N greater than 2 which identifies sequences of signal point subsets and the signal points of the identified signal point subsets are selected as a function of the second-level code. The first-level code is such that every different pair of identified sequences of signal point subsets differ in at least M subset positions where M is the desired level of time diversity, M greater than 1. The second-level code is such as to ensure that every different pair of valid sequences of signal points taken from the same sequence of signal point subsets differs in at least M signal point positions. This provides the overall multilevel coded modulation scheme with diversity M. Additionally, the minimum distance, as defined above, of the overall multilevel code is not increased by the use of the particular second-level code.
Advantageously, the increase in time diversity can be realized while suffering only a slight reduction in bandwidth efficiency. For example, a particularly advantageous embodiment of a multilevel code embodying the principles of the invention includes a four-dimensional, eight-state trellis code as the first-level code and a (2k+2, 2k) double parity check code as the second-level code using k=12 and using 2D 16-QAM as the constituent constellation. This embodiment exhibits a bandwidth efficiency of about 3 ⅓ bits/signal point, which is only slightly less than the bandwidth efficiency of 3 xc2xd bits/signal point achieved by a unilevel code using the same constellation but using only the first-level code. Moreover, it requires a decoder which is moderately more complex. However, the multilevel code exhibits a time diversity of xe2x80x9c2xe2x80x9d while the unilevel code exhibits only a time diversity of only M=1 (which, in actuality, means no time diversity), and it does so without sacrificing minimum distance. That is, as indicated below, the minimum distance of the overall code is not increased because of the presence of the second-level code. An advantageous trade-off is thus accomplished. By comparison, it may be possible to achieve a time diversity of M=2 using the same constellation to again achieve about the same bandwidth efficiency but employing a unilevel approach. Disadvantageously, however, such an approach will engender significantly higher decoder complexity as well as reduced minimum distance.
The prior art""s motivation for using multilevel coding has been to increase the minimum distance of the code, and thereby improve its error rate performance. It turns out that certain such prior art schemes may also achieve enhanced time diversity. (See for example, my U.S. Pat. No. 5,548,615 issued Aug. 20, 1996.) The invention here comprises the class of multilevel codes of the type described above not motivated by prior art considerations. That is, the invention here is that class of multilevel codes which provide diversity M greater than 1 but in which the minimum distance of the overall code is not increased by virtue of the presence of the second-level code.